Finite Group Databasebeta

← C2×#10591354 #11808192

Subgroups — C2×#10591354 #11808192

Order 1152.

2241 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#634C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C22×Dic3⋊Dic3C212yesmaximal
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×#63579C212yesmaximal
6#10591354C218yesmaximal, direct product factor
7C2×#4979—31nomaximal
8C2×#4656—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2212yes—
11C22×#634—24no—
12C22×#634—28no—
13C22×#634C2214yes—
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2212yes—
17C2×C3×Dic3⋊C4—24no—
18C2×C3×Dic3⋊C4C2214yes—
19C2×Dic3⋊Dic3—28no—
20C2×Dic3⋊Dic3C2218yes—
21C3×C3⋊#95C2214yes—
22#63579C2218yes—
23C23×Dic6—31no—
24C23×Dic6—31no—
25C23×Dic6—61no—
26C22×C3×C4⋊C4—31no—
27C22×C4⋊Dic3—32no—
28C22×Dic3⋊C4—32no—
29C22×Dic3⋊C4D311yescharacteristic
30C2×C3×#95—31no—
31C2×C3⋊#95—32no—
32C2×C3⋊#95—32no—
33C2×C3⋊#95D311yescharacteristic
34#4979—38no—
35#4656—38no—
36C24×C32C2311yescharacteristic
37C22×C32×C4—24no—
38C22×C32×C4D414yes—
39C22×C32×C4C2312yes—
40C22×C3⋊Dic3—24no—
41C22×C3⋊Dic3—24no—
42C22×C3⋊Dic3D418yes—
43C22×C3⋊Dic3C2314yes—
44C2×#634—232no—
45C2×#634—28no—
46C2×#634—216no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—24no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—24no—
53C22×C3×Dic3Q814yescomplemented
54C22×C3×Dic3Q818yescomplemented
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2314yes—
58C3×Dic3⋊C4—28no—
59Dic3⋊Dic3—216no—
60C2×#395—91noSylow
61C23×C3×C4—21no—
62C23×C3×C4—31no—
63C23×C3×C4—32no—
64C23×C3×C4—31no—
65C23×C3×C4C2×D311yescharacteristic
66C23×C3×C4C2×D311yescharacteristic
67C23×Dic3—32no—
68C23×Dic3—32no—
69C23×Dic3—62no—
70C23×Dic3C2×D311yescharacteristic
71C23×Dic3C2×D311yescharacteristic
72C23×Dic3C2×D312yes—
73C22×Dic6—34no—
74C22×Dic6—34no—
75C22×Dic6—64no—
76C22×Dic6—68no—
77C22×Dic6—68no—
78C22×Dic6—616no—
79C22×Dic6—68no—
80C22×Dic6—64no—
81C22×Dic6—64no—
82C2×C3×C4⋊C4—34no—
83C2×C3×C4⋊C4—64no—
84C2×C4⋊Dic3—38no—
85C2×C4⋊Dic3—68no—
86C2×Dic3⋊C4—24no—
87C2×Dic3⋊C4—38no—
88C2×Dic3⋊C4—68no—
89C2×Dic3⋊C4C2×D314yes—
90C3×#95—34no—
91C3⋊#95—38no—
92C3⋊#95—38no—
93C3⋊#95C2×D314yes—
94C23×C32C2×D412yes—
95C23×C32C2×D414yes—
96C23×C32C2×Q814yes—
97C23×C32C2×Q812yes—
98C23×C32#4112yes—
99C23×C32C2411yescharacteristic
100C2×C32×C4—28no—
101C2×C32×C4—24no—
102C2×C32×C4C2×D414yes—
103C2×C3⋊Dic3—216no—
104C2×C3⋊Dic3—24no—
105C2×C3⋊Dic3—24no—
106C2×C3⋊Dic3C2×D418yes—
107#634—232no—
108C2×C3×Dic3—216no—
109C2×C3×Dic3—28no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—44no—
117C2×C3×Dic3C2×Q814yescomplemented
118C2×C3×Dic3C2×Q818yescomplemented
119C23×Q8—91no—
120C22×C4⋊C4—31no—
121C22×C4⋊C4—92no—
122#395—98no—
123C2×#95—31no—
124C2×#95—92no—
125C24×C3—21no—
126C24×C3C22×D311yescharacteristic
127C24×C3C22×D311yescharacteristic
128C22×C3×C4—28no—
129C22×C3×C4—24no—
130C22×C3×C4—24no—
131C22×C3×C4—24no—
132C22×C3×C4—22no—
133C22×C3×C4—38no—
134C22×C3×C4—34no—
135C22×C3×C4—32no—
136C22×C3×C4—34no—
137C22×C3×C4—32no—
138C22×C3×C4—62no—
139C22×C3×C4—64no—
140C22×C3×C4—64no—
141C22×C3×C4—62no—
142C22×C3×C4—62no—
143C22×C3×C4—64no—
144C22×C3×C4D1214yes—
145C22×C3×C4#6714yes—
146C22×C3×C4C22×D312yes—
147C22×C3×C4C22×D312yes—
148C22×Dic3—22no—
149C22×Dic3—24no—
150C22×Dic3—24no—
151C22×Dic3—22no—
152C22×Dic3—24no—
153C22×Dic3—22no—
154C22×Dic3—38no—
155C22×Dic3—38no—
156C22×Dic3—34no—
157C22×Dic3—34no—
158C22×Dic3—68no—
159C22×Dic3—64no—
160C22×Dic3—68no—
161C22×Dic3—68no—
162C22×Dic3—64no—
163C22×Dic3—64no—
164C22×Dic3—64no—
165C22×Dic3—64no—
166C22×Dic3Dic618yescomplemented
167C22×Dic3Dic614yescomplemented
168C22×Dic3C22×D312yes—
169C22×Dic3C22×D312yes—
170C22×Dic3C22×D314yes—
171C2×Dic6—616no—
172C2×Dic6—616no—
173C2×Dic6—632no—
174C2×Dic6—664no—
175C2×Dic6—632no—
176C2×Dic6—632no—
177C2×Dic6—616no—
178C2×Dic6—68no—
179C2×Dic6—68no—
180C3×C4⋊C4—68no—
181C4⋊Dic3—616no—
182Dic3⋊C4—28no—
183Dic3⋊C4—616no—
184C22×C32#12014yes—
185C22×C32C22⋊Q818yes—
186C22×C32C22⋊Q814yes—
187C22×C32C4⋊Q814yes—
188C22×C32C4⋊Q818yes—
189C22×C32C22×D411yescharacteristic
190C22×C32C22×D412yes—
191C22×C32C22×Q812yes—
192C22×C32C22×Q811yescharacteristic
193C22×C32C2×#4111yescharacteristic
194C32×C4—24no—
195C3⋊Dic3—28no—
196C3×Dic3—28no—
197C3×Dic3—24no—
198C3×Dic3—42no—
199C22×Q8—94no—
200C22×Q8—188no—
201C22×Q8—184no—
202C23×C4—31no—
203C23×C4—32no—
204C23×C4—31no—
205C23×C4—92no—
206C23×C4D3211yescharacteristic
207C2×C4⋊C4—34no—
208C2×C4⋊C4—64no—
209C2×C4⋊C4—98no—
210C2×C4⋊C4—188no—
211#95—34no—
212#95—98no—
213C23×C3—21no—
214C23×C3—22no—
215C23×C3—24no—
216C23×C3—22no—
217C23×C3—22no—
218C23×C3—24no—
219C23×C3C2×Dic614yes—
220C23×C3C2×Dic612yes—
221C23×C3C2×D1212yes—
222C23×C3#23512yes—
223C23×C3D3×D414yes—
224C23×C3D3×D414yes—
225C23×C3#23712yes—
226C23×C3D3×Q812yes—
227C23×C3D3×Q814yes—
228C23×C3C2×#6712yes—
229C23×C3C23×D311yescharacteristic
230C23×C3C23×D311yescharacteristic
231C2×C3×C4—28no—
232C2×C3×C4—216no—
233C2×C3×C4—28no—
234C2×C3×C4—28no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—24no—
238C2×C3×C4—38no—
239C2×C3×C4—34no—
240C2×C3×C4—616no—
241C2×C3×C4—68no—
242C2×C3×C4—62no—
243C2×C3×C4—64no—
244C2×C3×C4—64no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—64no—
248C2×C3×C4—124no—
249C2×C3×C4C2×D1214yes—
250C2×C3×C4C2×#6714yes—
251C2×Dic3—216no—
252C2×Dic3—28no—
253C2×Dic3—22no—
254C2×Dic3—24no—
255C2×Dic3—24no—
256C2×Dic3—22no—
257C2×Dic3—24no—
258C2×Dic3—22no—
259C2×Dic3—38no—
260C2×Dic3—38no—
261C2×Dic3—44no—
262C2×Dic3—68no—
263C2×Dic3—68no—
264C2×Dic3—68no—
265C2×Dic3—632no—
266C2×Dic3—616no—
267C2×Dic3—616no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—64no—
271C2×Dic3—64no—
272C2×Dic3C2×Dic618yescomplemented
273C2×Dic3C2×Dic614yescomplemented
274Dic6—664no—
275Dic6—632no—
276Dic6—632no—
277C2×C32#39518yescomplemented
278C2×C32C2×#12011yescharacteristic
279C2×C32C2×C22⋊Q812yes—
280C2×C32C2×C22⋊Q811yescharacteristic
281C2×C32C2×C4⋊Q811yescharacteristic
282C2×C32C2×C4⋊Q812yes—
283C24C2×D3211yescharacteristic
284C2×Q8—1816no—
285C2×Q8—1832no—
286C2×Q8—188no—
287C22×C4—24no—
288C22×C4—34no—
289C22×C4—32no—
290C22×C4—34no—
291C22×C4—38no—
292C22×C4—32no—
293C22×C4—62no—
294C22×C4—64no—
295C22×C4—62no—
296C22×C4—64no—
297C22×C4—62no—
298C22×C4—64no—
299C22×C4—94no—
300C22×C4—98no—
301C22×C4—184no—
302C22×C4—184no—
303C22×C4#62614yes—
304C22×C4C2×D3212yes—
305C4⋊C4—68no—
306C4⋊C4—1816no—
307C22×C3—21no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—22no—
312C22×C3—28no—
313C22×C3—24no—
314C22×C3—24no—
315C22×C3—28no—
316C22×C3—24no—
317C22×C3#86914yes—
318C22×C3#87818yes—
319C22×C3#88214yes—
320C22×C3#88818yes—
321C22×C3#88818yes—
322C22×C3#89618yes—
323C22×C3#89714yes—
324C22×C3#92414yes—
325C22×C3#93714yes—
326C22×C3#94414yes—
327C22×C3C22×Dic612yes—
328C22×C3C22×Dic611yescharacteristic
329C22×C3C22×D1211yescharacteristic
330C22×C3C2×#23511yescharacteristic
331C22×C3C2×D3×D412yes—
332C22×C3C2×D3×D412yes—
333C22×C3C2×#23711yescharacteristic
334C22×C3C2×D3×Q811yescharacteristic
335C22×C3C2×D3×Q812yes—
336C22×C3C22×#6711yescharacteristic
337C3×C4—28no—
338C3×C4—24no—
339C3×C4—24no—
340C3×C4—68no—
341C3×C4—64no—
342C3×C4—122no—
343Dic3—28no—
344Dic3—24no—
345Dic3—42no—
346Dic3—616no—
347Dic3—68no—
348Dic3—68no—
349C32C2×#39511yescharacteristic, complemented, Sylow
350C23D3×Dic612yes—
351C23D3×Dic614yes—
352C23#379512yes—
353C23C2×#62612yes—
354C23#381114yes—
355C23C22×D3211yescharacteristic
356Q8—1832no—
357C2×C4—24no—
358C2×C4—28no—
359C2×C4—34no—
360C2×C4—38no—
361C2×C4—62no—
362C2×C4—64no—
363C2×C4—62no—
364C2×C4—64no—
365C2×C4—68no—
366C2×C4—616no—
367C2×C4—62no—
368C2×C4—64no—
369C2×C4—98no—
370C2×C4—124no—
371C2×C4—184no—
372C2×C4—184no—
373C2×C4—1816no—
374C2×C4C2×#62614yes—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—22no—
378C2×C3—28no—
379C2×C3—21no—
380C2×C3—22no—
381C2×C3#465618yescomplemented
382C2×C3#497918yescomplemented
383C2×C3C2×#86911yescharacteristic
384C2×C3C2×#87812yes—
385C2×C3C2×#88211yescharacteristic
386C2×C3C2×#88812yes—
387C2×C3C2×#88812yes—
388C2×C3C2×#89612yes—
389C2×C3C2×#89711yescharacteristic
390C2×C3C2×#92411yescharacteristic
391C2×C3C2×#93711yescharacteristic
392C2×C3C2×#94411yescharacteristic
393C22#6384018yes—
394C22#6385714yes—
395C22#6386614yes—
396C22#6389618yes—
397C22#6398114yes—
398C22C2×D3×Dic611yescharacteristic
399C22C2×D3×Dic612yes—
400C22C2×#379511yescharacteristic
401C22C22×#62611yescharacteristic
402C22C2×#381112yes—
403C4—24no—
404C4—64no—
405C4—68no—
406C4—122no—
407C4—188no—
408C3—21no—
409C3C2×#465611yescharacteristic, complemented
410C3C2×#497911yescharacteristic, complemented
411C2#1059135418yesdirect product factor
412C2C2×#6384012yes—
413C2C2×#6385711yescharacteristic
414C2C2×#6386611yescharacteristic
415C2C2×#6389612yes—
416C2C2×#6398111yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#395
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
6. #10591354C2direct (N × H)
53. C22×C3×Dic3Q8semidirect
54. C22×C3×Dic3Q8semidirect
117. C2×C3×Dic3C2×Q8semidirect
118. C2×C3×Dic3C2×Q8semidirect
166. C22×Dic3Dic6semidirect
167. C22×Dic3Dic6semidirect
272. C2×Dic3C2×Dic6semidirect
273. C2×Dic3C2×Dic6semidirect
277. C2×C32#395semidirect
349. C32C2×#395semidirect
381. C2×C3#4656semidirect
382. C2×C3#4979semidirect
409. C3C2×#4656semidirect
410. C3C2×#4979semidirect
411. C2#10591354direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×#6342
C22×C3×Dic3⋊C42
C22×Dic3⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#105913542
C2×#49793
C2×#46563